3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up

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Alexandra McCoy
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1 3.1 Start Thinking Sketch two perpendicular lines that intersect at point. Plot one point on each line that is not. all these points and. onnect and to make. What type of figure do points,, and make? ould you ever plot points and to make a perpendicular segment to either original line? parallel segment? Explain your reasoning. 3.1 Warm Up Use the diagram. 1. What is another name for? 2. What is another name for EG? 3. What is another name for H? 4. Name all segments with endpoint. 5. Name one pair of opposite rays. 6. Name a point on. E F G H 3.1 umulative Review Warm Up The midpoint M and one endpoint of JK are given. Find the coordinates of the other endpoint. 1. M( 5, 2 ) and J( 6, 7) 2. M( 14, 5 ) and K( 1, 8) 3. M( 9, 1 ) and J( 3, 0) 78 Geometry opyright ig Ideas Learning, LL

2 Name ate 3.1 Practice In Exercises 1 4, use the diagram. 1. Name a pair of parallel lines. 2. Name a pair of perpendicular lines. 3. Is? Explain. 4. Is? Explain. In Exercises 5 8, identify all pairs of angles of the given type. 5. alternate interior 6. alternate exterior 7. corresponding 8. consecutive interior Is it possible to draw three lines in two planes such that all three lines are skew? Explain your reasoning. 10. How many pairs of consecutive interior angles do you have when two horizontal lines are intersected by a transversal? How many pairs of consecutive interior angles do you have when three horizontal lines are intersected by a transversal? How many pairs of consecutive interior angles do you have when n horizontal lines are intersected by a transversal? 11. The given markings show how the railroad ties on a railroad track are related to each other. a. Name two pairs of parallel lines. b. Name two pairs of perpendicular lines c. Name all pairs of consecutive interior angles. d. Name all pairs of corresponding angles. e. Name all pairs of alternate interior angles. f. Name all pairs of alternate exterior angles. opyright ig Ideas Learning, LL Geometry 79

3 Name ate 3.1 Practice In Exercises 1 6, use the diagram. 1. Name a pair of parallel lines. 2. Name a pair of perpendicular lines. c 3. Name a pair of skew lines. d 4. Name a pair of parallel planes. 5. Is line f parallel to line g? Explain. 6. Is line e perpendicular to line g? Explain. e f g In Exercises 7 11, classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles and and and and and Two planes are parallel and each plane contains a line. re the two lines skew? Explain your reasoning. 13. Use the figure to decide whether the statement is true or false. Explain your reasoning. a. The line containing the sidewalk and the line containing the center of the road are parallel to each other. b. The line containing the center of the road is skew to the line containing the crosswalk. c. The plane containing a stop sign is perpendicular to the plane containing the ground. 80 Geometry opyright ig Ideas Learning, LL

4 Name ate 3.1 Enrichment and Extension Pairs of Lines and ngles 1. If two parallel planes are cut by a third plane, are the lines of intersection parallel? Explain your reasoning and include a drawing. 2. raw line a parallel to line b. raw line c parallel to line b. What relationship appears to exist between lines a and c? Make a conjecture about two lines that are parallel to the same line. 3. raw line perpendicular to a line m. raw a line n perpendicular to line m. What relationship appears to exist between line and line n? Make a conjecture about two lines that are perpendicular to the same line. In Exercises 4 and 5, draw the figure described. 4. Lines and m are skew, lines and n are skew, and lines m and n are parallel. 5. Line is parallel to plane, plane is parallel to plane, and line is not parallel to plane. 6. List all possible answers for each. a. 1 and are corresponding angles. b. 13 and are corresponding angles. c. 14 and are consective interior angles. d. 4 and are consective interior angles. e. 7 and are alternate interior angles f. 17 and are alternate interior angles. g. 6 and are alterior exterior angles. h. 18 and are alternate exterior angles. opyright ig Ideas Learning, LL Geometry 81

5 Name ate 3.1 Puzzle Time What Has Foot On Each End nd One In The Middle? Write the letter of each answer in the box containing the exercise number. Fill in the blank. 1. Two lines are if and only if they are both vertical lines or they both have the same slope. 2. Two lines are if and only if one is vertical and the other is horizontal or the slopes of the lines are negative reciprocals of each other. 3. Two lines are if and only if their equations are equivalent. 4. Two lines are lines when they do not intersect and are not coplanar. 5. (n) is a line that intersects two or more coplanar lines at different points. Identify the type of the pairs of angles and 5 nswers G. unskew K. coincident H. conditional. alternate exterior angles I. transversal T. angular U. straight S. skew L. horizontal R. perpendicular 7. 1 and and and and N. lined angles T. vertical angles P. inverse angles. parallel. consecutive interior angles. revolving angles L. converse angles Y. alternate interior angles M. intersecting angles. corresponding angles 82 Geometry opyright ig Ideas Learning, LL

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines

Name Period GEOMETRY CHAPTER 3 Perpendicular and Parallel Lines Section 3.1 Lines and Angles GOAL 1: Relationship between lines Two lines are if they are coplanar and do not intersect. Skew lines. Two